Prepare Cake Batter: Preheat oven to 350°F (175°C). In a large bowl, beat eggs and sugar until pale and fluffy. Gradually add oil and milk, mixing until smooth. Sift in flour, cocoa, baking powder, and salt. Fold gently until fully combined.
Bake Cake: Pour batter into a greased 9×13-inch pan. Bake 35–40 minutes, or until a toothpick inserted comes out clean. Let cool completely.
Make Brigadier: In a saucepan over medium heat, combine sweetened condensed milk, cocoa, and butter. Cook, stirring constantly, until thickened (about 8–10 minutes). Let cool slightly.
Make White Cream: In a separate saucepan, mix sweetened condensed milk, milk, cornstarch, and butter. Cook over medium heat, stirring constantly, until thickened. Remove from heat and stir in vanilla extract. Let cool.
Assemble Cake: Slice the cooled chocolate cake horizontally if desired. Spread brigadier over the first layer, then top with white cream. Repeat layers if using multiple layers. Finish with a smooth layer of white cream on top. Sprinkle with chocolate sprinkles, if desired.
Serving and Storage Tips
